Optical shape sensing (OSS), also referred to as Fiber-Optic RealShape (FORS), is a useful technology to reconstruct a three-dimensional shape of a device, in particular elongated device. In case of medical appliances, such a device may be an interventional device, e.g. a catheter or guide wire, which is partially inserted into a patient's body and thus cannot be directly viewed with the user's eyes. With optical shape sensing using an optical shape sensing fiber integrated in the interventional device, the three-dimensional shape of the interventional device can be known and thus be made “visible” up to the tip of the device.
US 2012/0069347 A1 and U.S. Pat. No. 8,773,650 B2 provide an overview of optical shape sensing. The whole content of these documents is incorporated herein by reference.
In optical shape sensing, the cores of a spun multicore optical fiber are interrogated simultaneously by an interferometric distributed-sensing system that makes use of, e.g., Optical Frequency Domain Reflectometry (OFDR).
In OFDR, light from a tunable light source, e.g. laser source, is coupled into an optical fiber, and the reflected or backscattered light is made to interfere with light from the same light source that has traveled along a reference path. When the frequency of the light source is swept linearly in time, the interference between the light that is coming from a single fixed scattering point on the optical fiber and the reference light creates a detector signal that has a constant frequency, this frequency being proportional to the difference of the travel time of the light along the measurement path along the optical fiber and the reference path. As the propagation velocity of the light and the length of the reference path are known, the position of the scattering point can be computed from the observed frequency.
When multiple scatters are present in the optical measurement fiber, the detector signal will be a superposition of different frequencies, each frequency indicative of the position of the respective scatterer. A Fourier transform of the detector signal (a “scattering profile”) can be computed; in graphs of the amplitude and phase of the transform signal, the amplitude and phase of the different frequencies that are present in the detector signal (which corresponds to different scatterer positions) will be shown at their respective positions along the horizontal axis of the graph.
The amplitude and phase of the scattered light can be affected by external influences acting on the fiber. For example, when the fiber is deformed by external stresses, for example by bending the optical fiber, or when the temperature of the optical fiber is modified, effects will be seen on the phase and/or amplitude of the scattering profile. From a comparison of the scattering profile of the optical fiber in a deformed state to the scattering profile of the same optical fiber in an unstressed reference state, information can be obtained about the external influences on the fiber as a function of position along the optical fiber, i.e. the optical fiber can be used for distributed sensing.
An optical fiber used in optical shape sensing usually is a spun multicore fiber comprising a center core and one or more outer cores helically wound around the center core. External stresses lead to strain of the cores which in turn leads to optical path length changes of each core of the multicore fiber. The system for optical shape sensing is capable of detecting the optical path length changes of each core simultaneously over a range of positions along the fiber, through comparison of the scattering profiles of each core of a strained “shape” measurement and an unstrained “reference” measurement.
When a fiber is bent, a core on the outside of the bend experiences positive strain (elongation), while a core on the inside of the bend experiences negative strain (compression). With sufficient knowledge of the distances of the cores to the center of the optical fiber and of the angles between the cores as seen from the center of the fiber, the radius of curvature and the orientation (angular position) relative to the cores of the center of the local tangent circle can be determined from the magnitudes of the strain signals of the cores. The “local tangent circle” is also known as the “osculating circle” in the branch of mathematics dealing with the differential geometry of curves.
In order to reconstruct the shape of an optical fiber, it is necessary to know the radius of curvature and the (change of) orientation of the local tangent circle in space. From the strain signals obtained by the optical shape sensing measurement it is possible to obtain the radius of curvature and the (change of) orientation of the local tangent circle relative to the cores. Thus, for proper shape reconstruction a method of obtaining information about the orientation of the cores in the deformed optical fiber is required. This in turn requires knowledge of the orientation of the cores in the reference (unstrained) state, in addition to a method for obtaining the change of orientation of the cores in a shape (deformed state of the fiber) relative to the reference state of the fiber (not deformed state). In other words, to translate strain signals provided by the optical shape sensing measurement from the outer cores into bend and bend direction, the rotational position of an outer core must be determined with a high degree of accuracy.
If a method of determining the change of orientation of the cores in a shape relative to the reference is available, the orientation of the cores in the reference can be obtained by measuring a special shape, e.g. a flat spiral: a shape which has curvature everywhere and the centers of the tangent circles all lie in the same plane. From the bend signals the orientation of the tangent circles of the shape relative to the cores can be computed. As the orientation of the tangent circles of the flat spiral is fixed in space, the orientation of the cores in the flat spiral shape is thus known. As it was assumed that a method for determining the change of orientation of the cores in the flat spiral relative to the reference is available, the orientation of the cores in the reference can now be computed.
In the current state of the art, the method for determining the change of orientation of the cores in a shape relative to the reference makes use of a twist rate phase signal that is a linear combination of the strain signals of the individual cores of the multicore fiber. For a multicore fiber with ideal geometry (a central core in the exact center of the fiber, and outer cores all at the same distance from the center of the fiber, and spaced equidistant in angular position), the twist rate phase signal equals the average of the outer core strain signals minus the strain signal of the central core. This twist rate phase signal is by design not sensitive to axial strain (common to all cores) and temperature changes.
For non-ideal fiber geometry, a method is described in US 2012/0069347 A1 for generating a twist rate phase signal that is a linear combination with modified coefficients of the strain signals, such that the resulting twist rate phase signal is still not sensitive to axial strain and temperature changes.
When the fiber is twisted in a manner that increases the number of turns per unit length, the outer cores become longer while the length of the central core remains constant, giving rise to a non-zero twist rate phase signal. When the fiber is twisted in a manner that decreases the number of turns per unit length, the outer cores become shorter, giving rise to a twist rate phase signal of opposite sign.
To lowest order, the twist rate phase signal is proportional to the change in number of turns per unit length of the fiber, i.e. to the rate of change of the true twist angle. It is known, however, that the relationship between twist rate phase signal and the rate of change of the true twist angle is intrinsically nonlinear. For large twist rate changes, a second-order (i.e. quadratic) term in the relation between change of twist rate and the resulting change of core length needs to be considered, as indicated in U.S. Pat. No. 8,773,650 B2.
However, U.S. Pat. No. 8,773,650 B2 does not disclose how to calculate the second-order term in order to compensate for the nonlinearity of the dependency of the twist rate on the twist rate phase signal.
To obtain the true twist angle at a chosen point on the optical fiber—i.e. the change of orientation of the cores between shape and reference at the chosen point, as compared to their relative orientation at a starting point—the rate of change of the true twist angle will have to be integrated along the fiber from the starting point up to the chosen point. This integration which is necessary in order to obtain the true twist angle at a chosen point reveals in practice that simply considering a second-order term in the relation between the twist rate phase signal and the true twist rate does not lead to an accurate twist angle at a chosen point along the optical fiber.
Thus, there is still a need in an improved method and system for obtaining a twist rate from the measured twist rate phase signal in order to arrive at accurate twist angles after integration.